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Development of a thermal equilibrium in a closed system over time through a heat flow that levels out temperature differences. Two physical systems are in thermal equilibrium if there is no net flow of thermal energy between them when they are connected by a path permeable to heat. Thermal equilibrium obeys the zeroth law of thermodynamics. A ...
A few different types of equilibrium are listed below. Thermal equilibrium: When the temperature throughout a system is uniform, the system is in thermal equilibrium. Mechanical equilibrium: If at every point within a given system there is no change in pressure with time, and there is no movement of material, the system is in mechanical ...
The steady-state heat equation for a volume that contains a heat source (the inhomogeneous case), is the Poisson's equation: = where u is the temperature, k is the thermal conductivity and q is the rate of heat generation per unit volume.
[63] This illustrates the importance for thermodynamics of the concept of temperature. Thermal equilibrium is achieved when two systems in thermal contact with each other cease to have a net exchange of energy. It follows that if two systems are in thermal equilibrium, then their temperatures are the same. [64]
Thus, the two systems are in thermal equilibrium with each other, or they are in mutual equilibrium. Another consequence of equivalence is that thermal equilibrium is described as a transitive relation: [7]: 56 [10] If A is in thermal equilibrium with B and if B is in thermal equilibrium with C, then A is in thermal equilibrium with C.
(Note - the relation between pressure, volume, temperature, and particle number which is commonly called "the equation of state" is just one of many possible equations of state.) If we know all k+2 of the above equations of state, we may reconstitute the fundamental equation and recover all thermodynamic properties of the system.
An equilibrium state is mathematically ascertained by seeking the extrema of a thermodynamic potential function, whose nature depends on the constraints imposed on the system. For example, a chemical reaction at constant temperature and pressure will reach equilibrium at a minimum of its components' Gibbs free energy and a maximum of their entropy.
The relation is generally expressed as a microscopic change in internal energy in terms of microscopic changes in entropy, and volume for a closed system in thermal equilibrium in the following way. d U = T d S − P d V {\displaystyle \mathrm {d} U=T\,\mathrm {d} S-P\,\mathrm {d} V\,}